How to Evaluate a Logarithm

Step-by-step solution

1. Turn the logarithm into a power question.

   $$2^y = 32$$

   Why: A logarithm asks: to what power do I raise the base?

2. Write 32 as a power of 2.

   $$32 = 2^5$$

   Why: 2 times 2 times 2 times 2 times 2 is 32.

3. Match the exponents.

   $$2^y = 2^5 \Rightarrow y = 5$$

   Why: Equal powers with the same base have equal exponents.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

1. 1

   $\log_2 16$

   Show answer

   $4$

2. 2

   $\log_3 27$

   Show answer

   $3$

3. 3

   $\log_{10} 1000$

   Show answer

   $3$

4. 4

   $\log_5 125$

   Show answer

   $3$

5. 5

   $\log_2 1$

   Show answer

   $0$